feat(mall): authenticate against the live API

Wave 2 of replacing the fixed-data mock adapter: the auth domain joins the live
list, so credentials, roles and tokens belong to the real user.

- session: validate a restored token through /auth/me instead of trusting
  localStorage, clearing it on 401/403 but keeping it when the API is merely
  unreachable; the route guard now uses the validated session
- login: report a 401 as invalid credentials rather than a generic failure, and
  drop the 6-character client rule so the API owns the password policy
- register: raise the rule to the API's 8 characters, remove the
  verification-code field (its button only counted down and the value was never
  sent), and report a duplicate email (409) distinctly
- TopBar and the user profile render their session-dependent branch client-only:
  validating the session before hydration made those localStorage-backed
  branches report hydration mismatches the previous code did not

Verified against the running backend: wrong password rejected, real JWT issued,
/user reachable, a short password refused with no network call, duplicate email
reported, a tampered token cleared and bounced to sign-in, a stale token kept
when the API is down, and the fixed-data rollback still signs in with the
backend stopped.

Also re-cuts docs/TBD-migrate-wave.md: auth is done, and cart, orders,
shipments and invoices must move together, because the mock adapter keeps their
state in one shared object and a partial flip fails at checkout.

OpenSpec change: openspec/changes/replace-mock-api-wave-2

apps/mall/pages/user.vue

@@ -36,7 +36,8 @@ function isActive(to: string): boolean {
         <div class="profile">
           <img src="/mock/avatar.svg" :alt="t('user.title')" />
           <div class="profile-copy">
-            <strong>{{ session.user?.display_name }}</strong>
+            <!-- Session lives in localStorage, so the name is unknown at SSR time. -->
+            <ClientOnly><strong>{{ session.user?.display_name }}</strong></ClientOnly>
             <NuxtLink to="/user">{{ t("user.editProfile") }}</NuxtLink>
           </div>
         </div>